The wedge was commonly used by attacking legionaries, - legionaries formed up in a triangle, the front 'tip' being one man and pointing toward the enemy, - this enabled small groups to be thrust well into the enemy and, when these formations expanded, the enemy troops were pushed into restricted positions, making hand-to-hand fighting difficult. This is where the short legionary gladius was useful, held low and used as a thrusting weapon, while the longer Celtic and Germanic swords became impossible to wield.

The Wedge

The saw was opposite tactic to the wedge. This was a detached unit, immediately behind the font line, capable of fast sideways movement down the length of the line to block any holes which might appear to develop a thrust where there might be a sign of weakness. In the case of two Roman armies fighting each other in a civil war, one might say that the 'saw' inevitably was the response to a 'wedge' by the other side.

The skirmishing formation was a widely spaced line up of troops, as opposed to the tighter packed battle ranks so typical of legionary tactics. It allowed for greater mobility and would have found many uses in the tactical handbooks of Roman generals.

Skirmishing Formation

The order to repel cavalry brought about a the following formation. The first rank would form a firm wall with their shields, only their pila protruding, forming a vicious line of glistening spearheads ahead of the wall of shields. A horse, however well trained, could hardly be brought to break through such a barrier. The second rank of the infantry would then use its spears to drive off any attackers whose horses came to a halt. This formation would no doubt prove very effective, particularly against ill-disciplined enemy cavalry.

Repel Cavalry

The orb is a defensive postition in the shape of a circle taken by a unit in desperate straits. It allows for a reasonably effective defence even if parts of an army have been divided in battle and would have required a very high level discipline by the individual soldiers.

The Orb

Here are seven specific instructions by Vegetius regarding the layout before battle:

1

On level ground the force is drawn up with a centre, two wings and reserves in the rear. The wings and reserves must be strong enough to prevent any enveloping or outflanking manoeuvre.

2

An oblique battle line with the left wing held back in a defensive position while the right advances to turn the opponent's left flank. Opposition to this move is to strengthen your left wing with cavalry and reserves, but if both sides are successful the battle front would tend to move in an anti-clockwise direction, the effect of which would vary with the nature of the ground. With this in mind it is as well to attempt to stabilize the left wing with the protection of rough or impenetrable ground, while the right wing should have unimpeded movement.

3

The same as No 2 except that the left wing is now made the stronger and attempts a turning movement and is to be tried only when it is known that the enemy's right wing is weak.

4

Here both wings are advanced together, leaving the centre behind. This may take the enemy by surprise and leave his centre exposed and demoralized. If, however, the wings are held, it could be a very hazardous manoeuvre, since your army is now split into three separate formations and a skillful enemy could turn this to advantage.

5

The same tactic as No 4, but the centre is screened by light infantry or archers who can keep the enemy centre distracted while the wings engage.

6

This is a variation of No 2 whereby the centre and left wing are kept back while the right wing attempts a turning movement. If it is successful, the left wing, reinforced with reserves, could advance and hop to complete the enveloping movement which should compress the centre.

7

This is the use of suitable ground on either flank to protect it, as suggested in No 2

All these tactics have the same purpose , that of breaking the enemy battle line. If a flank can be turned, the the strong centre has to fight on two fronts or is forced to fight in a restricted space. Once an advantage like this has been gained it is very difficult to correct the situation. Even in the highly trained Roman Army it would have been difficult to change tactics during the course of the battle and the only units which can be successfully deployed are those in the reserves or that part of the line not yet engaged. Thus the most important decision a general had to make concerned the disposition of the troops. If a weakness could be detected in the enemy line, it was exploited by using a stranger force to oppose it. Likewise, it was necessary to disguise one's battle line - even troops were disguised to delude the enemy. Often the very size of the army was skillfully hidden, troops packing tightly together to make it appear small, or spreading out to appear large. There were also many examples of surprise tactics made by detaching a small unit which suddenly emerged from a hidden place with much dust and noise to make the enemy believe that reinforcements had arrived.

Vegetius (Frontinus) is full of the oddest stratagems to mislead the enemy or demoralize his troops.
Once the enemy cracked, however, they were not to be surrounded, but an easy escape route left open. The reasons for this were that trapped soldiers would fight to the death but if they could get away, they would, and were exposed to the cavalry waiting on the flanks.

This important section of Vegetius closes with the tactics to be used in the case of a withdrawal in the face of the enemy. This highly difficult operation requires great skill and judgement. Both your own men and those of the enemy need to be deceived. It is suggested that your troops be informed that their retirement is to draw the enemy into a trap and the movement can be screened from the enemy with the use of cavalry across the front. Then the units are drawn off in a regular manner, but these tactics can only be employed if the troops have not yet been engaged. During a retreat units are detached and left behind to ambush the enemy if there is a hasty or incautious advance, and in this way tables can often be turned.

On a wider front, the Romans used tactics of denying their opponents the means of sustained warfare.
For this they employed the tactic of vastatio. It was in effect the systematic revaging of an enemy's territory. Crops were destroyed or carried off for Roman use, animals were taken away or simply slaughtered, people were massacred or enslaved.
The enemy's lands were decimated, denying his army any form of support. Sometiems these tactics were also used to conduct punitive raids on barbarian tribes which had performed raids across the border.
The reasons for these tactics were simple. In the case of punitive raids they spread terror among the neighbouring tribes and acted as a deterrent to them. In the case of all-out war or the quashing rebels in occupied territories these harsh tactics denied any enemy force the support they needed to sustain a lengthy struggle.

An example based on a force of 20 small warbands (bandae), or 4600 cavalrymen.Though in greater or lesser numbers, and with infantry or not, it is likely the Byzantine army would fight in similar array.

The main force would be the Fighting Line (ca. 1500 men) and the Supporting Line (ca. 1300 men).
The Supporting Line might have gaps in it to allow the Fighting Line to widthdraw through if necessary.
The Wings (2 x 400 men), also called the liers-in-wait tried to get behind or into the flank of the enemy in a sweeping move around the forces, far out of sight.
The Flanks (2 x 200 men) either side of the main Fighting Line were meant to prevent the enemy's wings or flanks from circling one's own force. Often the right Flank was also used to attack the side of the opponent's main body. Striking from the right it drove into the left of the opponent which was harder to defend as most warriors would bear their weapons with their right arm.
At the back of the force a Third Line or Reserve (ca. 500 men) would be posted out to the sides, ready either to help defend the Flanks, to help steady any forces of the Fighting Line driven back through the Supporting Line, or to intervene in any flanking assaults on the enemy.
This leaves the general's own escort which would most likely lie to rear of the force and would consist of about 100 men.